Is this priority or parity!

$N$ integers $1, 2, 3, \ldots N$ are placed on a circle in clockwise order such that $i$ and $(i+1)$ are adjacent for all $1 \leq i \leq N - 1$, and $1$ and $N$ are also adjacent. Given an integer $K$, Ashish repeatedly removes integers from the circle until only one integer remains. He does so in the following manner. In each move, Ashish finds the integer which is on the $K$-th place from the s